In the figure shown there are two semicircles of radii $r_{1}$ and $r_{2}$ in which a current i is flowing. The magnetic induction at the centre O will be

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Solution

The correct option is C
The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards.

$∴ B = B_{1} + B_{2} = \frac{μ_{0} i}{4 r_{1}} + \frac{μ_{0} i}{4 r_{2}} = \frac{μ_{0} i}{4} (\frac{r_{1} + r_{2}}{r_{1} r_{2}}) \otimes$

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In the figure shown there are two semicircles of radii r1 and r2 in which a current i is flowing. The magnetic induction at the centre O will be

The correct option is C The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards. ∴ B = B1 + B2 = μ0i4r1 + μ0i4r2 = μ0i4(r1+r2r1r2)⊗

In the figure shown there are two semicircles of radii $r_{1}$ and $r_{2}$ in which a current i is flowing. The magnetic induction at the centre O will be

The correct option is C
The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards.

$∴ B = B_{1} + B_{2} = \frac{μ_{0} i}{4 r_{1}} + \frac{μ_{0} i}{4 r_{2}} = \frac{μ_{0} i}{4} (\frac{r_{1} + r_{2}}{r_{1} r_{2}}) \otimes$